Implement linearized version of baseband phase-locked loop
The Linearized Baseband PLL block is a feedback control system that automatically adjusts the phase of a locally generated signal to match the phase of an input signal. Unlike the Phase-Locked Loop block, this block uses a baseband model method. Unlike the Baseband PLL block, which uses a nonlinear model, this block simplifies the computations by using x to approximate sin(x). The baseband PLL model depends on the amplitude of the incoming signal but does not depend on a carrier frequency.
This PLL has these three components:
An integrator used as a phase detector.
A filter. You specify the filter's transfer function using the Lowpass filter numerator and Lowpass filter denominator parameters. Each is a vector that gives the respective polynomial's coefficients in order of descending powers of s.
To design a filter, you can use functions such as butter, cheby1, and cheby2 in Signal Processing Toolbox™ software. The default filter is a Chebyshev type II filter whose transfer function arises from the command below.
[num, den] = cheby2(3,40,100,'s')
A voltage-controlled oscillator (VCO). You specify the sensitivity of the VCO signal to its input using the VCO input sensitivity parameter. This parameter, measured in Hertz per volt, is a scale factor that determines how much the VCO shifts from its quiescent frequency.
This block accepts a sample-based scalar input signal. The input signal represents the received signal. The three output ports produce:
The output of the filter
The output of the phase detector
The output of the VCO
The numerator of the lowpass filter transfer function, represented as a vector that lists the coefficients in order of descending powers of s.
The denominator of the lowpass filter transfer function, represented as a vector that lists the coefficients in order of descending powers of s.
This value scales the input to the VCO and, consequently, the shift from the VCO's quiescent frequency.
For more information about phase-locked loops, see the works listed in Selected Bibliography for Synchronization in Communications System Toolbox™ User's Guide.